Many European countries have free monthly passes for poor people and I haven't noticed any problems of that kind.

Nor do I actually see what's particularly "unethical" about riding free public transport when it's cold outside? If capacity on rolling stock is tight, four square feet of floor in a warm room should be eminently affordable for the world's richest country. And, no, the availability of shelters doesn't make homelessness so comfortable that it becomes a lifestyle choice, or do you know anybody who would want to exchange their job & home for a homeless shelter?